U.S. Pat. No. 4,348,081 discloses a projection system with a high brightness by using lenses having aspheric surfaces. However, the length of the light beam progress path from the face glass of the CRT to a screen in the disclosed projection system is so long that it is not suitable for a compact projection set. In general, if a lens consists of a glass material, it produces a spherical aberration rather than a color aberration, and if it consists of a plastic material, it produces color aberration rather than spherical aberration. Since the lens in the disclosed projection system in U.S. Pat. No. 4,348,081 is aspherical, it consists of the plastic material and therefore color aberration is present. Color aberration is increased in accordance with the light beam progress path, and the color aberration is increased in the disclosed projection system.
The relationship between the focus distortion by thermal variation and the focal length or the relationship between the color aberration and the focal length are as follows. Assuming that the thickness of the lens is negligible in FIG. 1, the following equations are obtained. EQU 1/a+1/b=1/f (1) EQU 1/f=(N-1) (1/r.sub.1 -1/r.sub.2) (2)
where
a is the distance between lens 1 and the phosphor surface of CRT 2, PA0 b is the distance between lens 1 and screen 3, PA0 f is the focal length of lens 1, PA0 r.sub.1 and r.sub.2 are curvature radii of lens 1. PA0 N is the refractive index. PA0 F is the F number of lens 1, PA0 M is the magnification of lens 1, PA0 .alpha. is the common elevation angle for both the beam spot and lens 1.
Since the characteristics of the projection system is affected less by the fluctuation for the curvature radius, which is caused by the fluctuation of the lens shape caused by the thermal fluctuation, than the fluctuation for the refractive index which is caused by the fluctuation of the lens shape, and since fluctuation caused by curvature radius may be cancelled with the fluctuation for the lens barrel if they consist of plastic materials, equation (3) is obtained from equation (2) by neglecting the terms including r.sub.1 and r.sub.1. EQU .delta.f/f=.delta.N/(N-1) (3)
Deviation .delta. d for the diametered of the beam spot projected on screen 3 is defined by following equation (4). EQU .delta.d=.delta.b*.alpha.p=.delta.b/(F*M) (4)
where
From equation (1)-(4) EQU d=((1+M).sup.2 * f/(F*M))*(.delta.N/(N-1)) (5)
As appearing equation (5), d is proportioned to focal length f, therefore the aberration corresponding to diamater d of the beam spot is reduced if flocal length f is shortened.